A “Pseudo-excitation” approach for structural damage identification: From “Strong” to “Weak” modality

A damage characterization framework based on the “pseudo-excitation” (PE) approach has recently been established, aimed at quantitatively identifying damage in beam-, plate-, and shell-like structural components. However, it is envisaged that the effectiveness of the PE approach can be restricted in practical implementation, due to the involvement of high-order derivatives of structural dynamic deflections, in which measurement noise and uncertainties can overwhelm the damage-associated signal features upon mathematical differentiation. In this study, the PE approach was revamped by introducing the weighted integration, whereby the prerequisite of satisfying the local equilibrium conditions was relaxed from “point-by-point” to “region-by-region”. The revamped modality was thus colloquially referred to as “weak formulation” of the PE approach, as opposed to its original version which is contrastively termed as “strong formulation”. By properly configuring a weight function, noise immunity of the PE approach was enhanced, giving rise to improved detection accuracy and precision even under noisy measurement conditions. Furthermore, the ‘weak formulation’ was extended to a series of coherent variants through partial integration, rendering a multitude of detection strategies by selecting measurement parameters and configurations. This endowed the PE approach with flexibility in experimental manipulability, so as to accommodate various detection requirements. As an application of the “weak formulation”, a continuous gauss smoothing (CGS)-based detection scheme was developed, and validated by localizing multiple cracks in a beam structure, showing fairly improved noise tolerance.